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Revert vandalism to version by Hellacioussatyr |
→Mean, variance and covariance: add name of property |
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Given a [[probability space]] <math>\textstyle (\Omega, \mathcal F, \operatorname{P})</math> with <math>A \in \mathcal F</math>, the indicator random variable <math>\mathbf{1}_A \colon \Omega \rightarrow \mathbb{R}</math> is defined by <math>\mathbf{1}_A (\omega) = 1 </math> if <math> \omega \in A,</math> otherwise <math>\mathbf{1}_A (\omega) = 0.</math>
;[[Mean]]: <math>\operatorname{E}(\mathbf{1}_A (\omega)) = \operatorname{P}(A) </math> (also called "Fundamental Bridge").
;[[Variance]]: <math>\operatorname{Var}(\mathbf{1}_A (\omega)) = \operatorname{P}(A)(1 - \operatorname{P}(A)) </math>
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